Publication Type
Journal Article
Version
submittedVersion
Publication Date
8-2021
Abstract
We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Hölder classes as special cases. The general Glivenko-Cantelli theorem is then applied in more concrete high-frequency statistical settings to establish uniform convergence results for general integrated functionals of the volatility of efficient price and local moments of microstructure noise.
Keywords
Glivenko-Cantelli, high-frequency data, spot volatility, microstructure noise, occupation measure
Discipline
Econometrics | Probability
Research Areas
Econometrics
Publication
Annals of Applied Probability
Volume
31
Issue
4
First Page
1914
Last Page
1943
ISSN
1050-5164
Identifier
10.1214/20-AAP1637
Publisher
Institute of Mathematical Statistics
Citation
LI, Jia; ZHANG, Congshan; and LIU, Yunxiao.
Glivenko-Cantelli Theorems for integrated functionals of stochastic processes. (2021). Annals of Applied Probability. 31, (4), 1914-1943.
Available at: https://ink.library.smu.edu.sg/soe_research/2535
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1214/20-AAP1637